Finite Group Databasebeta

← #14761619

Subgroups — #14761619

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic
2#13077041C211yesmaximal, characteristic
3#13069561C211yesmaximal, characteristic, complemented
4#13069389C211yesmaximal, characteristic, complemented
5#13069212C211yesmaximal, characteristic, complemented
6#13069212C211yesmaximal, characteristic, complemented
7#13068890C211yesmaximal, characteristic
8#13068890C211yesmaximal, characteristic
9#13068633C211yesmaximal, characteristic
10#13068501C211yesmaximal, characteristic, complemented
11#13068496C211yesmaximal, characteristic, complemented
12#13068488C211yesmaximal, characteristic, complemented
13#13068462C211yesmaximal, characteristic
14#13068455C211yesmaximal, characteristic
15C11×#2961C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19C4×#4339C2211yescharacteristic
20C11×#446—21no—
21C11×#446—21no—
22C11×#446—21no—
23C11×#446—21no—
24C11×#424C2211yescharacteristic
25C11×#424C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C11×#405C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32C2×#66886C2211yescharacteristic
33C2×#66886C2211yescharacteristic
34#10622714C2211yescharacteristic
35#10622714C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622707C411yescharacteristic, complemented
39#10622704C411yescharacteristic, complemented
40#10622700C411yescharacteristic, complemented
41#10622697C411yescharacteristic, complemented
42#10622679C411yescharacteristic, complemented
43#10622679C411yescharacteristic, complemented
44#10622676C411yescharacteristic, complemented
45#10622676C411yescharacteristic, complemented
46#10622615C2211yescharacteristic
47#10622615C2211yescharacteristic
48#10622611C2211yescharacteristic
49#10622611C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C4×#4318C2211yescharacteristic
53#10622321—21no—
54#10622321—21no—
55#10622320—21no—
56D11×#97—21no—
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#125C2×C411yescharacteristic
75C11×#125C2×C411yescharacteristic
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C11×#117C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2311yescharacteristic
86C2×C4⋊Dic11—21no—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90C2×#4318C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66954—22no—
94#66954—22no—
95#66954—22no—
96#66954Q814yescomplemented
97C2×#4313—21no—
98C2×#4313—21no—
99C2×C8×D11—21no—
100C2×C8×D11—21no—
101C4×D44C2×C411yescharacteristic
102C4×D44C2×C411yescharacteristic
103#66925—21no—
104C42×D11—21no—
105C4×Dic22C2×C411yescharacteristic
106C4×Dic22C2×C411yescharacteristic
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×#97—21no—
114C11×#97—21no—
115C11×#97D411yescharacteristic
116C11×#97D411yescharacteristic
117C11×#97D411yescharacteristic
118C11×#97D411yescharacteristic
119C4×C8×C11—21no—
120C4×C8×C11—21no—
121C11⋊#95—21no—
122#66889—22no—
123#66889—22no—
124#66886—22no—
125#66886—22no—
126#66879—21no—
127#66879—21no—
128#66879—22no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11—22no—
132#66874C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66873C2×C411yescharacteristic
140#66872C2×C411yescharacteristic
141#66872C2×C411yescharacteristic
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66871C2×C411yescharacteristic
145#66871C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148C4⋊(C11⋊C8)C2×C411yescharacteristic
149C4⋊(C11⋊C8)C2×C411yescharacteristic
150C4⋊(C11⋊C8)C2×C411yescharacteristic
151C4⋊(C11⋊C8)C2×C411yescharacteristic
152#66867—21no—
153C4×C11⋊C8—21no—
154#21629—111nomaximal, Sylow
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163#4339—21no—
164#4339—21no—
165#4339C2×Q812yes—
166#4339#4112yes—
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×Dic22C22×C411yescharacteristic
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×Q812yes—
185C2×C8×C11#4112yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11C22×C411yescharacteristic
201C42×C11C22×C411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C22⋊Dic11—21no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—21no—
207C4⋊Dic11—42no—
208C4⋊Dic11C22×C411yescharacteristic
209C4⋊Dic11C22×C411yescharacteristic
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219#4318—21no—
220#4318—21no—
221#4318C2×Q812yes—
222#4318#4112yes—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8C22×C411yescharacteristic
230C2×C11⋊C8C22×C411yescharacteristic
231C2×C11⋊C8C22×C411yescharacteristic
232C2×C11⋊C8C22×C411yescharacteristic
233#4313—24no—
234#4313—24no—
235C8×D11—24no—
236C8×D11—24no—
237#3076—111no—
238#2961D1111yescharacteristic, complemented
239#2875—111no—
240#1986—111no—
241#1950—111no—
242#1922—111no—
243#1922—111no—
244#1866—111no—
245#1866—111no—
246#1806—111no—
247#1773—111no—
248#1772—111no—
249#1771—111no—
250#1765—111no—
251#1764—111no—
252C23×C11C2×#4111yescharacteristic
253C22×D11—21no—
254Q8×C11—81no—
255Q8×C11—81no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C22⋊D11—22no—
273C22⋊D11—22no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283D44—21no—
284D44C4×Q812yes—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—81no—
288C4×D11—81no—
289Dic22—21no—
290Dic22C4×Q812yes—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11C22⋊Q812yes—
296C8×C11C22⋊Q812yes—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—21no—
301C11⋊C8—22no—
302C11⋊C8—22no—
303C2×#131—111no—
304C2×#131—111no—
305#533C2×D1111yescharacteristic
306C4×#41—111no—
307#479—111no—
308#479—111no—
309#478—111no—
310#478—111no—
311#477—111no—
312#476—111no—
313#475—111no—
314#474—111no—
315#446—21no—
316#446—21no—
317#446—21no—
318#446—21no—
319C2×#108—111no—
320C2×#108—111no—
321#427—111no—
322#427—111no—
323#424C2×D1111yescharacteristic
324#424C2×D1111yescharacteristic
325#423C2×D1111yescharacteristic
326C2×C4⋊C8—111no—
327C2×#104—111no—
328C2×#104—111no—
329#416—111no—
330#416—111no—
331#405—111no—
332#405—111no—
333#405—221no—
334#405—221no—
335#405C2×D1111yescharacteristic
336#405C2×D1111yescharacteristic
337C4×M16—111no—
338C4×M16—221no—
339C2×#97—111no—
340C2×#97—221no—
341C2×#97C2×D1111yescharacteristic
342C2×C4×C8—111no—
343C4×C4⋊C4—111no—
344#341—111no—
345#341—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#339—111no—
352#336—111no—
353#336—111no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11#52911yescharacteristic
358C22×C11#53311yescharacteristic
359C2×D11—22no—
360C2×D11—41no—
361C2×D11—41no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11C2×C4×Q811yescharacteristic
371C4×C11C4×#4111yescharacteristic
372C4×C11C2×C22⋊Q811yescharacteristic
373C4×C11#52511yescharacteristic
374Dic11—22no—
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379C2×#41—111no—
380#131—114no—
381#131—222no—
382#131—222no—
383#131—222no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—221no—
393C22×C8—221no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8C4×D1111yescharacteristic
397C4⋊Q8C4×D1111yescharacteristic
398#125C4×D1111yescharacteristic
399#125C4×D1111yescharacteristic
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—111no—
405C4×Q8—111no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410#117—111no—
411#117—221no—
412#117C22×D1111yescharacteristic
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—221no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#108—222no—
420#108—222no—
421#107—111no—
422#107—111no—
423#107—111no—
424#107—111no—
425#106—111no—
426#106—111no—
427#106—111no—
428#106—111no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439#104—222no—
440#104—222no—
441#103—111no—
442#103—111no—
443#103—111no—
444#103—111no—
445#102—111no—
446#102—111no—
447#102—111no—
448#102—111no—
449#97—21no—
450#97—21no—
451#97—222no—
452#97—221no—
453#97—221no—
454#97—221no—
455#97C22⋊D1111yescharacteristic
456#97C22⋊D1111yescharacteristic
457#97C22⋊D1111yescharacteristic
458#97C22⋊D1111yescharacteristic
459C4×C8—21no—
460C4×C8—21no—
461C4×C8—222no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—221no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11C4×C22⋊Q811yescharacteristic
469C2×C11#295611yescharacteristic
470C2×C11#295711yescharacteristic
471D11—42no—
472#41—112no—
473#41—112no—
474#41—221no—
475#41—221no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—111no—
479C2×D4—111no—
480C2×D4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4#433911yescharacteristic
487C22×C4#433911yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—112no—
494M16—112no—
495M16—224no—
496M16—221no—
497M16—221no—
498M16—224no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—224no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—224no—
515C2×C8Q8×D1112yes—
516C2×C8#434312yes—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C2×C8C2×C22⋊D1111yescharacteristic
520C2×C8C2×C22⋊D1111yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—111no—
528C4⋊C4—111no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42C2×C4×D1111yescharacteristic
551C42C2×C4×D1111yescharacteristic
552C42C2×C22⋊D1111yescharacteristic
553C42C2×C22⋊D1111yescharacteristic
554C11#2162911yescharacteristic, complemented, Sylow
555C23—221no—
556C23C2×#433911yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—112no—
560Q8—221no—
561D4—112no—
562D4—222no—
563D4—222no—
564D4—221no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—221no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—881no—
583C2×C4—881no—
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4C4×C22⋊D1111yescharacteristic
587C2×C4C4×C22⋊D1111yescharacteristic
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×Q8×D1111yescharacteristic
590C2×C4C2×#434311yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—222no—
599C8—222no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—221no—
604C8#6699912yes—
605C8#6699912yes—
606C22—21no—
607C22—21no—
608C22—222no—
609C22—441no—
610C22—441no—
611C22#1062310911yescharacteristic
612C22#1062311111yescharacteristic
613C22C2×C4×C22⋊D1111yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—222no—
623C4—442no—
624C4—441no—
625C4—441no—
626C4—881no—
627C4C4×Q8×D1111yescharacteristic
628C4C4×#434311yescharacteristic
629C4C2×#6699911yescharacteristic
630C4#1062335911yescharacteristic
631C2—21no—
632C2—21no—
633C2—442no—
634C2C4×#6699911yescharacteristic
635C2#1307752311yescharacteristic
636C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2961C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#2961D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13069561C2semidirect
4. #13069389C2semidirect
5. #13069212C2semidirect
6. #13069212C2semidirect
10. #13068501C2semidirect
11. #13068496C2semidirect
12. #13068488C2semidirect
15. C11×#2961C2semidirect
38. #10622707C4semidirect
39. #10622704C4semidirect
40. #10622700C4semidirect
41. #10622697C4semidirect
42. #10622679C4semidirect
43. #10622679C4semidirect
44. #10622676C4semidirect
45. #10622676C4semidirect
96. #66954Q8semidirect
238. #2961D11semidirect
554. C11#21629semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130783982
#130770412
#130695612
#130693892
#130692122
#130688902
#130686332
#130685012
#130684962
#130684882
#130684622
#130684552
C11×#29612
#2162911